Question

How do we measure financial risk best? Why is this such an important exercise today, especially for financial institutions?

Answer 1

Risk and risk measure are terms that have no unique definition and usage. It would be natural to measure risk in terms of probability distributions. But often it is useful to express risk with one number. Mappings from spaces of probability distributions or random variables into the real numbers are called risk measures. The process involves identifying the amount of risk involved and either accepting or mitigating the risk associated with an investment. Some common measures of risk are standard deviation, beta, value at risk (VaR) and conditional value at risk.

Variance and standard deviation were historically the dominating risk measures in finance. Standard deviation measures the dispersion of data from its expected value. The standard deviation is used in making an investment decision to measure the amount of historical volatility, or risk, associated with an investment relative to its annual rate of return. It indicates how much the current return is deviating from its expected historical normal returns. For example, a stock that has a high standard deviation experiences higher volatility, and therefore, a higher level of risk is associated with the stock.

Beta is another common measure of risk. Beta measures the amount of systematic risk a security has relative to the whole market. The market has a beta of 1, and it can be used to gauge the risk of a security. If a security's beta is equal to 1, the security's price moves in time step with the market. A security with a beta greater than 1 indicates that it is more volatile than the market. Conversely, if a security's beta is less than 1, it indicates that the security is less volatile than the market. For example, suppose a security's beta is 1.5. In theory, the security is 50% more volatile than the market.

The VaR is a statistical measure used to assess the level of risk associated with a portfolio or company. The VaR measures the maximum potential loss with a degree of confidence for a specified period. For example, suppose a portfolio of investments has a one-year 10% VaR of $5 million. Therefore, the portfolio has a 10% chance of losing more than $5 million over a one-year period.

The Value-at-Risk (VaR) at level ? ? (0, 1) of a loss variable L is defined as the ?-quantile of the loss distribution:

VaR_?(L) = q_?(L) = inf{l : P(L ? l) ? ?}.

Conditional VaR is another risk measure used to assess the tail risk of an investment. The conditional VaR assesses the likelihood, with a certain degree of confidence, that there will be a break in the VaR. This measure is used as an extension to the VaR and seeks to assess what happens to an investment beyond its maximum loss threshold. This measure is more sensitive to events that happen in the tail end of a distribution, also known as tail risk. For example, suppose a risk manager believes the average loss on an investment is $10 million for the worst 1% of possible outcomes for a portfolio. Therefore, the conditional VaR, or expected shortfall, is $10 million for the 1% tail.

It is important to measure Rislk especially to the financial Institutions because,

• It is not possible to know the gravity of risks unless the risks are measured and quantified.
• The criticality of a risk is the factor that obliges resource units and forces costs to be spent on it.
• A metric is created based on the potential and features of a risk in an organization. This allows to review success, failure or developments, and analyse the efficiency of risk control measures.
• Measuring risks provides clarity on the choice of actions and decisions that should enforce balance in the risk-reward trade-off (wherein the degree of risk, high or low, is directly proportional to the return).

Basically, risk metrics and measurements give an option to mitigate risks as well as open businesses towards risk opportunities.